Exam 3: Polynomial and Rational Functions

Use the factor theorem to find the polynomial of degree 4 having zeroes , , x = 3 + i, x = 3 - i. Assume a lead coefficient of 1.

Factor completely. Then state the multiplicity of the roots and the degree of P. P(x) = x³ - 2x² - 15x + 36.

Use the following to answer questions : p(x) = x⁴ - 5x³ + 5x² + 5x - 6 -Use the information gathered, testing for 1 and -1, synthetic division, and the factor theorem to factor p completely.

Complete the square to write the function in shifted form. f(x) = x² + 7x + 1

State the degree and end behavior of the function. f(x) = (x - 1)⁶(x + 3)(x - 3)³

Use the Guidelines for Graphing Polynomial Functions to graph the polynomial. f(x) = x³ - 4x² + x + 6

Graph the polynomial function. f(x) = x⁴ + 3x³ - 3x² - 11x - 6

Use the following to answer questions : y varies directly with x; y = 8.4 when x = 24. -Complete the table.

Solve the inequality using a number line and the behavior of the graph at each zero. Write your answer in interval notation. (x + 3)(x - 4) < 0

Graph the function using the Guidelines for Graphing Rational Functions, which is simply modified to include nonlinear asymptotes. Clearly state all intercepts and asymptotes and any additional points used to sketch the graph.

Use the following to answer questions : A varies directly with B and inversely with C squared, and A = 93.75 when B = 20 and C = 1.2. -Complete the table.

Find all rational zeroes of the function given and use them to write the function in factored form. Use the factored form to state all zeroes of the function. Begin by applying the tests for 1 and -1. p(x) = 4x⁴ + x³ + 33x² +9x - 27

Determine the nonlinear asymptote if it exists.

State the end behavior of the function. f(x) = -3x⁵ + 5x⁴ + x² - 2x + 2

Use the following to answer questions : (Gridlines are spaced one unit apart.) -State the equations of the horizontal and vertical asymptotes.

State the end behavior of the function. f(x) = 5x⁴ + 2x³ - 5x² - 5x - 3

Use the following to answer questions : A varies directly with B and inversely with C squared, and A = 93.75 when B = 20 and C = 1.2. -Find the constant of variation.

Use the following to answer questions : y varies directly with x; y = 8.4 when x = 24. -Write the variation equation.

Use the Guidelines for Graphing Rational Functions to graph .

Use the following to answer questions : An automobile manufacturer can produce up to 300 cars per day. The profit made from the sale of these vehicles can be modeled by the function , where P(x) is the profit in dollars and x is the number of automobiles made and sold. -Find the y-intercept and explain what it means in this context.